Question

name:
date:
period:
segment addition postulate color by number
instructions: solve for x and determine the missing length. show all of your work on the sheet provided. develop a model when one is not given for all word problems. circle the correct answer choice and color. color the corresponding problem number in the picture provided.
solve for x

1. if points l, m, and n are collinear with m between l and n. develop a model.

ln = 15, mn = -1 + x, and lm = 3x - 4
x = 6 black
x = 5 dark purple
x = 16 light blue
2.
x + 12
7 + x
x = -3 white
x = 1 dark blue
x = 6 dark green

1. if points k, l, and m are collinear with l between k and m. develop a model.

km = x + 18, lm = 2x + 18, and kl = 7
x = -11 grey
x = -2 light green
x = -7 black
4.
x + 11
x + 5
x = 0 dark blue
x = 5 light purple
x = 11 white

1. if points j, k, and l are collinear with k between j and l. develop a model.

kl = x + 17, jk = 4, and jl = 2x + 32
x = -13 light blue
x = -14 dark green
x = -11 grey
© sarah davis, 2022

Explanation:

Step1: Postulado de adición de segmentos

Por el postulado, $LN = LM + MN$

Step2: Sustituir valores dados

$15 = (3x - 4) + (-1 + x)$

Step3: Simplificar la ecuación

$15 = 3x - 4 -1 + x$
$15 = 4x - 5$

Step4: Despejar el término con $x$

$4x = 15 + 5$
$4x = 20$

Step5: Calcular valor de $x$

$x = \frac{20}{4} = 5$

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Step1: Postulado de adición de segmentos

Por el postulado, $QS = QR + RS$

Step2: Sustituir valores dados

$13 = (x + 12) + (7 + x)$

Step3: Simplificar la ecuación

$13 = x + 12 + 7 + x$
$13 = 2x + 19$

Step4: Despejar el término con $x$

$2x = 13 - 19$
$2x = -6$

Step5: Calcular valor de $x$

$x = \frac{-6}{2} = -3$

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Step1: Postulado de adición de segmentos

Por el postulado, $KM = KL + LM$

Step2: Sustituir valores dados

$x + 18 = 7 + (2x + 18)$

Step3: Simplificar la ecuación

$x + 18 = 2x + 25$

Step4: Despejar el término con $x$

$x - 2x = 25 - 18$
$-x = 7$

Step5: Calcular valor de $x$

$x = -7$

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Step1: Postulado de adición de segmentos

Por el postulado, $RT = RS + ST$

Step2: Sustituir valores dados

$16 = (x + 11) + (x + 5)$

Step3: Simplificar la ecuación

$16 = x + 11 + x + 5$
$16 = 2x + 16$

Step4: Despejar el término con $x$

$2x = 16 - 16$
$2x = 0$

Step5: Calcular valor de $x$

$x = \frac{0}{2} = 0$

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Step1: Postulado de adición de segmentos

Por el postulado, $JL = JK + KL$

Step2: Sustituir valores dados

$2x + 32 = 4 + (x + 17)$

Step3: Simplificar la ecuación

$2x + 32 = x + 21$

Step4: Despejar el término con $x$

$2x - x = 21 - 32$

Step5: Calcular valor de $x$

$x = -11$

Answer:

1. $x = 5$ (Dark Purple)
2. $x = -3$ (White)
3. $x = -7$ (Black)
4. $x = 0$ (Dark Blue)
5. $x = -11$ (Grey)